(1) Mobile Backup and Restore by Avast

Mobile Backup and Restore is an application by Avast Software, one of the leading anti-virus and security software. Mobile Backup and Restore lets you backup all your contacts, videos, photos and numerous other data and keeps them secured on the cloud. This app automatically backs up all your data and various settings on a specific date and time. The backed up data can be browsed and restored at a later time with optional PIN protection. This app also has a premium version that gives you a number of additional backup options and features.

Key features of Mobile Backup and Restore app are:

  • Backup SMS and Contacts, call logs and photos.
  • Premium app lets you backup music, videos, apps.
  • Backup settings for rooted phones.
  • Easy in-app upgrade.

(2) Helium App Sync and Backup

Helium is an ultimate app to backup Android phone apps and data to SD card or in cloud storage. With this app, you can sync app data from additional Android devices and schedule automatic app backups without losing any data. And to use Helium, you do not require rooting your Android phone. You can backup from your phone as well as from your pc. Helium also offers a premium version of the app which includes automatic backup, backup schedules and cloud backup and restore from popular cloud storage services like Dropbox, Box and Google Drive.

I have been personally using Titanium and I’ve found it the best way to backup my Android phone. For using Titanium, you need a rooted Android phone. With Titanium, you can backup your data and apps which include system apps and protected apps plus the additional data on your SD card. The backups work without interrupting any services or any ongoing operation on your Android device. You can move any data to or from the SD card and browse the app’s data. Titanium also has a pro version which contains a number of incredible features:
  • Keep multiple backups for each app.
  • Backup and restore sms, call logs, mms, WiFi AP as XML and bookmarks.
  • Multi-user app data.
  • Sync from the cloud including Box, Google Drive and Dropbox.
  • Convert user apps to system apps.
  • ‘Destroy all Market links’ feature.
  • Encryption.
  • Dalvik cache cleaner.
  • Unlimited schedules.

(4) Easy Backup and Restore

Easy backup and restore app stores all your sms, mms, call logs, bookmarks, calendar and contacts and helps you backup Android phone to Google. With this app, you can backup the apps in your SD card or any cloud storage platforms like Dropbox, Gmail, Google Drive, OneDrive or Box. You can either backup manually or schedule for automatic backups. Main features of the Easy Backup and Restore app are:
  • View backup contents.
  • Email the backed up contents.
  • Backup apps to SD card or cloud storage platforms.
  • Backs up from rooted Android phones.
  • Backup and restore app data and batch restore apps (only on rooted phones).

(5) GCloud Backup

GCloud is a free Android phone backup app which is safe and keeps your private data secured. You can even easily migrate to separate devices and expand your storage by saving everything in the cloud. Not only this, you can organize your files and easily access them without searching too much for any file. Key features of GCloud Backup app are:

  • Automatically backup messages, call logs, contacts, documents, settings and photos.
  • Backup WhatsApp, camera, Viber images and videos.
  • Automatic uploads.
  • Password protection to secure your data.
  • No rooting required.
  • Restore and migrate to new device easily.

(6) App Backup and Restore

App Backup and Restore is a free app and the best program to backup Android phone. This app allows you to save space by removing the apps which are not required on your phone. The main features of the App Backup and Restore app are:
  • Switch apps between WiFi and Bluetooth.
  • Backup apps to SD card.
  • Backup market links for protected apps.
  • Batch backup and restore.
  • Show storage usage.
  • Multi version backup.
  • Send .apk file via email.
  • Share market link.
  • App manager.

(7) Super Backup: SMS and Contacts

Super Backup is one among the fastest and performs the best backup for Android. With Super Backup, you can restore apps, contacts, sms, call logs, bookmarks and calendars to your SD card, as well as to cloud storage platforms like Google Drive and Gmail. The key features of Super Backup app are:
  • Backup and restore app’s data and apps from SD card (for rooted phones)
  • Batch restore apps from SD card (for rooted phones)
  • Backup and restore calendars, bookmarks, sms, call logs and contacts to and from SD card.
  • Schedule automatic backups
  • Auto upload scheduled backups to Gmail or Google Drive
  • Download backed up files from Google Drive
  • Super Backup app also has a pro version which is available for Rs. 126.68 only at the Play Store.

(8) TruBackup

truBackup is a free backup and restore app for Android that easily backs up your contacts, mms, sms, apps, photos, videos and helps transfer your data between different carriers and devices. You can also schedule automatic backups with truBackup and backup your data to SD card, Google Drive and Dropbox.

(9) CM Backup

CM Backup is a safe and simple free backup and restore tool for Android that stores all your mobile data into the cloud and it is considered as the best app to backup Android. On downloading the app, you’ll get 5GB free cloud storage. CM Backup is a secure app that won’t let you worry about your data and you can avail them even if your device is lost or stolen. The main features of CM Backup app are:
  • Backup and restore contacts, sms, mms, photos, bookmarks, calendars, alarm and dictionary.
  • Secure data transfer (SSL) 
  • Compress photos
  • View backed up items on the web
  • Supports Multilanguage
  • No rooting required

(10) My Backup

My Backup is a free and the good backup and restore app for android devices that securely stores all your Android phone data. The main features of My Backup app are:
  • Backup and restore data to your SD card or local device
  • Backup data to cloud servers including Dropbox
  • Transfer data between two devices
  • Schedule multiple backups to multiple locations
  • View backup details
  • Multilanguage support
  • Trigger backups remotely from their website to begin on your device

(11) Ultimate Backup

Ultimate Backup is a free and the best Android backup app that performs multiple tasks like backup and restore, freeze, uninstall apps, sync data to the cloud, kill tasks and includes lots of functionality. Key features of Ultimate Backup app are:
  • Backup calls logs, bookmarks, sms, WiFi.
  • Backup to cloud storage services like Dropbox, Google Drive and Box.
  • Freeze system and user apps.
  • App uninstaller
  • Task manager
  • Transform user apps to system apps and vice versa.
  • Connect apps to Google Play and set up automatic updates
  • Send and share apps
  • Explore app data and Google Play details
  • Schedule backups
  • Restore data from cloud
  • Auto backup and delete
  • Kill apps at boot 
  • Ad free interface

(12) GO Backup and Restore

GO Backup and Restore is a professional tool that stores all your Android phone data including system settings, apk files, app data, sms, call logs, etc. It securely stores your data without letting you worry about them and easily restores them without any changes. The main features of GO Backup and Restore app are:
  • Batch backup and restore data including call logs, calendar, contacts, bookmark, etc.
  • Merge individual backups
  • Batch delete backups
  • Backup data in cloud storage like Google Drive and Dropbox.
  • Schedule automatic backups
  • View backup history

(13) AppMonster Free Backup Restore

AppMonster is a free and the best backup and restore app for Android phones and tablets that offer features like batch backup and restore, uninstall apps from SD card, share and do lots with it. The app supports multiple languages and includes a lot of features like,
  • Downgrade any app on your phone
  • Backup and restore apps to and from SD card
  • Quick uninstall any app
  • Automatic backup
  • Share app links on social media sites like Facebook and Twitter
  • Send backed up apps (.apk files) via email or Dropbox.

(14) SMS Backup+

SMS Backup+ is specifically developed to backup sms, mms and call logs by using a separate label in Gmail or Google Calendar and you can easily restore them back to the phone. Although the automatic backup feature might not work if the SMSBackup+ app is installed on your SD card. SMS Backup+ does not include the most advanced features like the other apps but still you can use it for taking the basic backups on your Android device.